If a number N is expressed in binary by using only 'ones,' what can
you say about its square (in binary)?

Golden Fibs

Stage: 5 Challenge Level:

This is straightforward but care must be taken to explain the
significance of both roots of the quadratic equation. Also you must
prove both the 'if' and the 'only if', that is, for general
Fibonacci sequences, 'if the first two terms are in the golden
ratio then the sequence is geometric' and 'if the sequence is
geometric then the ratio of successive terms is the golden
ratio'.

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